Creating a custom property with named values
Check this code, this shows you 2 different options:

One is with direct control over the index with a slider with changing labels,
The other one is with the EnumProp like you have it.



import bpy

from bpy.props import EnumProperty

def updateEnumParameter(self, context):
    context.object.my_list_index = int(self.face)
    print(self.face)

class cls_IntFloatString(bpy.types.PropertyGroup):
    face_items =(("0","None","none"),
                 ("1","Smile","smile"),
                 ("2","Content","content"),
                 ("3","Dizzy","dizzy"),
                 ("4","Cat","cat"),
                 ("5","Girl","girl"),
                 ("6","Yuck","yuck"),
                 ("7","Macho","macho"),
                 ("8","Pixel","pixel"),
                 ("9","Charming","charming"),
                 ("10","Cry","cry"),
                 ("11","Ouch","ouch"),
                 ("12","Ultraman","ultraman"))
    face = bpy.props.EnumProperty(items=face_items, update=updateEnumParameter)

bpy.utils.register_class(cls_IntFloatString)

faces = {
    '0': "None",
    '1': "Smile",
    '2': "Content",
    '3': "Dizzy",
    '4': "Cat",
    '5': "Girl",
    '6': "Yuck",
    '7': "Macho",
    '8': "Pixel",
    '9': "Charming",
    '10': "Cry",
    '11': "Ouch",
    '12': "Ultraman"}

# Add these properties to every object in the entire Blender system
bpy.types.Object.my_list_index = bpy.props.IntProperty(min=0, max=len(faces)-1, default=0)
bpy.types.Object.my_list = bpy.props.PointerProperty(type=cls_IntFloatString)

class IntFloatStringPanel(bpy.types.Panel):
    bl_label = "Int Float String"
    bl_idname = "OBJECT_PT_hello"
    bl_space_type = "PROPERTIES"
    bl_region_type = "WINDOW"
    bl_context = "object"

    def draw(self, context):
        layout = self.layout
        box = layout.box()
        row = box.row()
        row.label("Selected Face:")
        row.prop(context.object, 'my_list_index', text=faces[str(context.object.my_list_index)], slider=True)
        box.prop(context.object.my_list, 'face', text='Selected Face')

def register():
    bpy.utils.register_class(IntFloatStringPanel)

def unregister():
    bpy.utils.unregister_class(IntFloatStringPanel)

if __name__ == "__main__":
    register()